The graph in the image shows a line with a negative slope crossing the y-axis and x-axis at specific points. To find the equation of the line, we can use the slope-intercept form of a linear equation, which is:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept (the point where the line crosses the y-axis).

Step 1: Identify two points on the line.

From the graph, two clear points on the line are:

• $(0, 6)$, which is the y-intercept.
• $(4, 0)$, which is the x-intercept.

Step 2: Calculate the slope $m$.

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(0, 6)$ and $(4, 0)$:

$m = \frac{0 - 6}{4 - 0} = \frac{-6}{4} = -\frac{3}{2}$

Step 3: Write the equation.

Now that we have the slope $m = -\frac{3}{2}$ and the y-intercept $b = 6$, the equation of the line is:

$y = -\frac{3}{2}x + 6$

This is the equation of the line in slope-intercept form.

Let me know if you'd like further details or have any questions!

Related Questions:

1. How do you find the slope from a graph if no clear points are given?
2. What is the point-slope form of a line equation, and how does it relate to the slope-intercept form?
3. How do you convert the equation from slope-intercept form to standard form?
4. What does the slope tell us about the direction of the line?
5. How can you verify if a point lies on a line given its equation?

Tip: Always check your points carefully when calculating the slope, especially for signs (positive or negative).